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Currently displaying 1 – 12 of 12

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On BVPs in l(A).

Gerd HerzogRoland Lemmert — 2005

Extracta Mathematicae

We prove the existence of extremal solutions of Dirichlet boundary value problems for u'' + f(t,u,u') = 0 in l(A) between a generalized pair of upper and lower functions with respect to the coordinatewise ordering, and for f quasimonotone increasing in its second variable.

Second order differential inequalities in Banach spaces

Gerd HerzogRoland Lemmert — 2001

Annales Polonici Mathematici

We derive monotonicity results for solutions of ordinary differential inequalities of second order in ordered normed spaces with respect to the boundary values. As a consequence, we get an existence theorem for the Dirichlet boundary value problem by means of a variant of Tarski's Fixed Point Theorem.

On the positivity of semigroups of operators

Roland LemmertPeter Volkmann — 1998

Commentationes Mathematicae Universitatis Carolinae

In a Banach space E , let U ( t ) ( t > 0 ) be a C 0 -semigroup with generating operator A . For a cone K E with non-empty interior we show: ( )     U ( t ) [ K ] K ( t > 0 ) holds if and only if A is quasimonotone increasing with respect to K . On the other hand, if A is not continuous, then there exists a regular cone K E such that A is quasimonotone increasing, but ( ) does not hold.

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